{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZHKIY5TOSLIMAFGA7BLRAM6FUS","short_pith_number":"pith:ZHKIY5TO","schema_version":"1.0","canonical_sha256":"c9d48c766e92d0c014c0f8571033c5a4802d6a5023f12172b45052f9d0528443","source":{"kind":"arxiv","id":"1304.0513","version":2},"attestation_state":"computed","paper":{"title":"Separating OR, SUM, and XOR Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Janne H. Korhonen, Magnus Find, Matti J\\\"arvisalo, Mika G\\\"o\\\"os, Mikko Koivisto, Petteri Kaski","submitted_at":"2013-04-02T01:25:48Z","abstract_excerpt":"Given a boolean n by n matrix A we consider arithmetic circuits for computing the transformation x->Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative integers), and non-monotone XOR-circuits (addition modulo 2). Our focus is on \\emph{separating} these models in terms of their circuit complexities. We give three results towards this goal:\n  (1) We prove a direct sum type theorem on the monotone complexity of tensor product matrices. As a corollary, we obtain matrices that admit OR-circuits of size O(n), but "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1304.0513","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-04-02T01:25:48Z","cross_cats_sorted":[],"title_canon_sha256":"83ffa2e0cb084188a3be4ef32a952574b52b12f1217164e8ce4463850b83e81f","abstract_canon_sha256":"6ad78d7bd2fef044187e743abe9aeb4c2400f5872d027f00e20d671fe15f734d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:22.495598Z","signature_b64":"Gb6DdMnBttgOlMHrmU4ZRSfWD7KyvcthejZnG+MNJjk/flc0Ydxl6SPoSoSpA7ekF19CWeHLOFNrf3jX/ezEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9d48c766e92d0c014c0f8571033c5a4802d6a5023f12172b45052f9d0528443","last_reissued_at":"2026-05-18T03:27:22.495010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:22.495010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Separating OR, SUM, and XOR Circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Janne H. Korhonen, Magnus Find, Matti J\\\"arvisalo, Mika G\\\"o\\\"os, Mikko Koivisto, Petteri Kaski","submitted_at":"2013-04-02T01:25:48Z","abstract_excerpt":"Given a boolean n by n matrix A we consider arithmetic circuits for computing the transformation x->Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative integers), and non-monotone XOR-circuits (addition modulo 2). Our focus is on \\emph{separating} these models in terms of their circuit complexities. We give three results towards this goal:\n  (1) We prove a direct sum type theorem on the monotone complexity of tensor product matrices. As a corollary, we obtain matrices that admit OR-circuits of size O(n), but "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0513","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1304.0513","created_at":"2026-05-18T03:27:22.495104+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.0513v2","created_at":"2026-05-18T03:27:22.495104+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0513","created_at":"2026-05-18T03:27:22.495104+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZHKIY5TOSLIM","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZHKIY5TOSLIMAFGA","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZHKIY5TO","created_at":"2026-05-18T12:28:09.283467+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZHKIY5TOSLIMAFGA7BLRAM6FUS","json":"https://pith.science/pith/ZHKIY5TOSLIMAFGA7BLRAM6FUS.json","graph_json":"https://pith.science/api/pith-number/ZHKIY5TOSLIMAFGA7BLRAM6FUS/graph.json","events_json":"https://pith.science/api/pith-number/ZHKIY5TOSLIMAFGA7BLRAM6FUS/events.json","paper":"https://pith.science/paper/ZHKIY5TO"},"agent_actions":{"view_html":"https://pith.science/pith/ZHKIY5TOSLIMAFGA7BLRAM6FUS","download_json":"https://pith.science/pith/ZHKIY5TOSLIMAFGA7BLRAM6FUS.json","view_paper":"https://pith.science/paper/ZHKIY5TO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.0513&json=true","fetch_graph":"https://pith.science/api/pith-number/ZHKIY5TOSLIMAFGA7BLRAM6FUS/graph.json","fetch_events":"https://pith.science/api/pith-number/ZHKIY5TOSLIMAFGA7BLRAM6FUS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZHKIY5TOSLIMAFGA7BLRAM6FUS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZHKIY5TOSLIMAFGA7BLRAM6FUS/action/storage_attestation","attest_author":"https://pith.science/pith/ZHKIY5TOSLIMAFGA7BLRAM6FUS/action/author_attestation","sign_citation":"https://pith.science/pith/ZHKIY5TOSLIMAFGA7BLRAM6FUS/action/citation_signature","submit_replication":"https://pith.science/pith/ZHKIY5TOSLIMAFGA7BLRAM6FUS/action/replication_record"}},"created_at":"2026-05-18T03:27:22.495104+00:00","updated_at":"2026-05-18T03:27:22.495104+00:00"}